An empty tank is connected with pipes A, B and C. A and B are inlet pipes and they fill the tank in 6 hours and 8 hours respectively, while C is an outlet pipe and it empties the completely filled tank in 5 hours. Find the time in which the tank will be completely filled if all the pipes are opened together.

Solution(By Examveda Team)

Work rate of Pipe A = 100/6 = 16.66% per hour.
Work rate of Pipe B = 100/8 = 12.5% per hour.

Work rate (Negative) of Pipe C = 100/5 = 20% per hour.
So, Combined work rate of A, B and C,
= 16.66 + 12.50 - 20 = 9.16% per hour.
Time taken to fill the tank = 100/9.16 = 10.91 hours = 120/11 hours.

Alternatively you can Solve it through fractional method as well,

A fills = 1/6 part per hour.
B fills = 1/8 part per hour.
C empties = 1/5 part per hour.
Combined work,
= 1/6 + 1/8 - 1/5

= (20 + 15 - 24)/120 = 11/120 part per hour.
Time taken to completed the work = 120/11 hours.